Nick wants to buy a pair of shoes. the original cost of the shoes is $56.75, and the markup is 12 percent. how much will he have to pay for the shoes?
a. $6.81
b. $49.64
c. $63.56

1. The probability that exactly 12 students drive to school is 0.169.

2.The probability that more than 15 students drive to school is 0.027.

3. The probability that no more than 10 students drive to school is 0.004.

4. The mean and standard deviation of the sample are 13.6 and 2.4, respectively.

5. The percentage falling within 1 standard deviation of the mean is approximately 68%, which satisfies the empirical rule for normal distributions.

This problem involves the binomial distribution, since each student either drives to school (success) or does not (failure), and the probability of success is given as 0.68 for each student.

(1) The probability that exactly 12 students drive to school is given by the binomial probability mass function:

P(X = 12) \(= (20 choose 12) * (0.68)^12 * (1 - 0.68)^(20 - 12) = 0.169\)

(2) The probability that more than 15 students drive to school is given by the complement of the probability that at most 15 students drive to school:

P(X > 15) = 1 - P(X <= 15) = 1 - sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i)}\) for i = 0 to 15.

This is approximately 0.027.

(3) The probability that no more than 10 students drive to school is given by the cumulative distribution function:

P(X <= 10) = sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i}\) for i = 0 to 10. This is approximately 0.004.

(4) The mean of the binomial distribution is given by the formula np, where n is the sample size and p is the probability of success.

Thus, the mean is 200.68 = 13.6.

The standard deviation of the binomial distribution is given by the formula sqrt(np(1-p)), which is approximately 2.4.

(5) The percentage falling within one standard deviation of the mean is approximately 68% by the empirical rule, which is the same as the percentage of students who drive to school in the university.

However, the empirical rule applies to normal distributions, and the binomial distribution is not exactly normal.

Nonetheless, for large sample sizes, the binomial distribution can be approximated by a normal distribution using the central limit theorem, which would make the empirical rule applicable.

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Answer:

-8

Step-by-step explanation:

(-2)^3 X (-2)^7 / 3X 4^6

= (-8) X (-128) / (3 X 4096)

= 1024 X -128 / 12288

= -128/12

= -8/1

So the final answer is -8

Answer:

1.398101×10^6

Step-by-step explanation:

(-2)^3×(-2)^7/3 ×4^6

=4194304/3

=1.398101×10^6

The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.

Red region is x + y ≤ 11

Blue region is x + 2y ≤ 12

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Two systems of linear inequalities are:

x + y ≤ 11

x + 2y ≤ 12

The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.

Thus,

The graph of the system of inequalities is given below.

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The given equation has one solution which is x = 6 (which is a REAL number).

Linear Equation Solutions are the values of a variables in linear equations that give all possible solutions. Linear equations represent real-world problems by involving unknown quantities with in form with one or more variables.

Some key concepts regarding the solution of linear equation are-

Now, for the given question;

The linear equation is -

4x + 9 = 33

Solving this;

4x = 33 - 9

4x = 24

x = 24/4

x = 6

Therefore, the solution of the given linear equation is (x=6), where 6 is the real number.

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The complete question is-

The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)

4x + 9 = 33

Answer:

A) angle bisector

Step-by-step explanation:

The ray drawn theough angle BOA creates 2 congruent angles.

Answer:

(- 5, 5 )

Step-by-step explanation:

5x + 7y = 10 → (1)

- 9x + y = 50 ( add 9x to both sides )

y = 9x + 50 → (2)

substitute y = 9x + 50 into (1)

5x + 7(9x + 50) = 10

5x + 63x + 350 = 10 ( subtract 350 from both sides )

68x = - 340 ( divide both sides by 68 )

x = - 5

substitute x = - 5 into (2)

y = 9(- 5) + 50 = - 45 + 50 = 5

solution is (- 5, 5 )

The radius of the cylinder is approximately 5.17 inches

What is volume ?

Volume is a measure of the amount of space occupied by an object or a substance. It is usually expressed in cubic units, such as cubic meters, cubic centimeters, cubic inches, etc. The volume of a three-dimensional object, such as a cube, sphere, or cylinder, is calculated by measuring the length, width, and height or radius of the object and applying the appropriate formula. For example, the volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.

According to the question:
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the height h = 11 inches and the volume V = 1,692.46 cubic inches.

Plugging in these values to the formula, we get 1,692.46 = πr²(11).

Solving for r, we can divide both sides by π(11) and then take the square root: r = √(1,692.46/(11π)).

Using a calculator, we get r ≈ 5.17 inches (rounded to two decimal places).

Therefore, the radius of the cylinder is approximately 5.17 inches.


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The future value of the account in 2 years is $2226.15

The given variables can be represented as:

The Future value can be calculated using the formula given as

FV = P(1 + r/n)^nt

Also from the question, we have

n = 4

This is so because the investment is compounded 4 times in a year as a result of being compounded quarterly

Solving further, we replace the variables with their values in the above equation

FV = 1900 * (1 + 8%/4)^(4 * 2)

Evaluate

FV = 2226.15

Hence, the amount is $2226.15

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Answer:

36

Explanation:

Given the ratio:

Let the number = x

Then:

Next, solve for x:

Thus, the number that makes the ratio equivalent to 3:5 is 36.

Answer:

12/7

Step-by-step explanation:

The value of the expression as a fraction is 12/7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

6/7 ÷ 1/2

This can be written as,

= (6/7) / (1/2)

= (6 x 2)/7

= 12/7

Thus,

The value is 12/7.

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Answer:

630

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

To find the slope, you do y₂ - y₁ / x₂ - x₁

y₂ - y₁ / x₂ - x₁

= -35 - 11 / 5 - 1

= -24 / 4

= -6

The slope is -6

Answer:

-6

Step-by-step explanation:

Hi,

To find the slope when given a table, just pick two points, subtract the y values, and then divide them by the x values after you subtract them as well. Here's what I mean...

Let's use 1, -11 and 5, -35

So...

-35 - (-11)

This is the change in y. -35 - (-11) is the same thing as -35 + 11 (subtracting  negative switches to adding it)

You get -24

Now, the change in x.

5 - 1 = 4

So, -24/4 and you get the slope of : -6

I hope this helps :)

Answer:

I think Substitution

Step-by-step explanation:

Because x is already solved for in the second equation.

The difference quotient for the function \(f(x) = -\frac{1}{5x-12}\)  is \(\frac{5}{(5x+5h-12)(5x-12)};\) h≠0

Option B) is the correct answer.

Given that;

We know that difference quotient is expressed as;

\(\frac{f(x+h)-f(x)}{h}\)

Next, substitute x+h for x.

Hence;

\(f(x+h) = -\frac{1}{5(x+h)-12}\)

Now,

\(\frac{f(x+h)-f(x)}{h} = \frac{-\frac{1}{5(x+h)-12}-(-\frac{1}{5x-12}) }{h} \\\\= \frac{5}{(5x-12)(5h+5x-12)}\\\\= \frac{5}{(5x+5h-12)(5x-12)};\)h≠0

The difference quotient for the function \(f(x) = -\frac{1}{5x-12}\)  is \(\frac{5}{(5x+5h-12)(5x-12)};\) h≠0

Option B) is the correct answer.

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Answer:

\(2^{4}\)

Step-by-step explanation:

Answer:

2^4

Since the answer is 16.

The base area is 3x² + 10x  + 40  + 145 / (x -4).

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Given:

Volume of prism = 3x³-2x²-15

and, height = x-4

Now, Volume of prism = Base area x height

3x³-2x²-15 = (x- 4) x b

b =  3x³-2x²-15/ (x -4)

Now,

b =  3x³-12x² +10x² -40x +40x -160 + 145/ (x -4)

b= 3x²( x -4)+ 10x (x- 4) + 40(x -4) + 145

b = 3x² + 10x  + 40  + 145 / (x -4)

Hence, the base area is 3x² + 10x  + 40  + 145 / (x -4).

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Answer:

I have no idea

Step-by-step explanation:

The answer is B. x = 12

First, you must set up the equation.

\(4x+11=6x-13\)

Then, you must subtract 6x on both sides.

\(-2x+11=-13\)

Next, subtract 11 on both sides.

\(-2x=-24\)

Finally, divide -2 on both sides.

\(x=12\)

Answer:

x2-12x+68

Step-by-step explanation:

Answer:

c = -1

Step-by-step explanation:

3(c+5)=12

3 × c = 3c

3 × 5 = 15

3c + 15 = 12

     - 15   -15

   3c = -3

c = -3 ÷ 3 = -1

Check:

3(-1+5)=12

-3 + 15 = 12

Answer:

{x | x > –5}

{x | x > –3}

{x | x > 3}

{x | x > 5}

Step-by-step explanation:

9514 1404 393

Explanation:

We can find the slope by solving for y.

  3x +2y +7 = 5x +3y +10

  -2x -3 = y . . . . . . . . . . . . . add -5x-10-2y to both sides of the equation

In this form, the slope (m) is the coefficient of x, -2. Hence m = -2.

__

Alternate solution

A graph of the equation shows it has an x-intercept of -1.5 and a y-intercept of -3. The slope (m) is then "rise" divided by "run", or ...

  m = rise/run = -3/1.5

  m = -2

Answer:

68,5*4=274 nên cái ao đó là hình vuông

Step-by-step explanat

4*a là chu vi hình vuông

Answer:

y = 4x + 4

Step-by-step explanation:

If this equation is parallel to y = 4x + 2, that means it would have the same gradient. And since the y-intercept is stated, you just need to put it next to the gradient

Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:

The roots are

\(x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i\)

Step-by-step explanation:

4x² + 16x + 25 = 0

Using the quadratic formula

That's

\(x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\)

From the question

a = 4 , b = 16 , c = 25

Substitute the values into the above formula and solve

We have

\(x=\dfrac{-16\pm\sqrt{16^2-4(4)(25)} }{2(4)}\)

\(x=\dfrac{-16\pm\sqrt{256-400} }{8}\)

\(x=\dfrac{-16\pm\sqrt{-144} }{8}\)

\(x=\dfrac{-16\pm12 \ i}{8}\)

Separate the real and imaginary parts

That's

\(x=\dfrac{-16}{8}\pm\dfrac{12}{8} \ i\)

\(x=-2\pm\dfrac{3}{2} \ i\)

We have the final answer as

\(x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i\)

Hope this helps you

The equation of the line through the points (0, 9) and (3, 0) is y = -3x + 9.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line and m is the slope of the line.

First, we calculate the slope (m) using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Substituting the values (0, 9) and (3, 0), we get m = (0 - 9)/(3 - 0) = -9/3 = -3.

Next, we choose one of the points, let's say (0, 9), and substitute its coordinates into the point-slope form: y - 9 = -3(x - 0).

Simplifying the equation, we get y - 9 = -3x, or rearranging it, y = -3x + 9.

Therefore, the equation of the line passing through the points (0, 9) and (3, 0) is y = -3x + 9.

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